65. If 6 men, in 12 days, reap 18 acres of grain, how many acres will 12 men reap in 4 days? 66. What part of 1 month is 15 days? Is 1 day? Is 2 days? Is 3 days? Is 5 days? Is 10 days? Is 20 days? 67. What is the interest of $20 for 4 months? For 10 months? For 3 months? For 1 year 4 months? 68. What is the amount of $40 for 2 mo.? For 5 mo.? For 10 mo.? For 1 yr. 8 mo. ? 69. What is the interest of $60 for 15 days? For 1 day? For 5 days? For 2 mo. 15 days? days? For 1 yr. 8 mo. 15 days? For 10 days? 70. What must you pay a broker, who gives you $20 in Boston bills, in exchange for Providence bills, at per cent commission? At per cent.? At 1 per cent.? 71. What is my demand for selling $600 worth of cotton, and guarantying the payment, at 5 per cent. commission? At 7 per cent. commission? At 4 per cent.? 72. What is the amount of $1 for 1 yr. 8 mo. ? 73. What is the amount of $200 for 1 yr. 8 mo. ? 74. What, then, is the present worth of $220, due 1 yr. 8 mo hence? 75. What is the present worth of $530, due 1 yr. hence? What is the discount? 76. A merchant, having bought cloth for 50 cents a yard, wishes to mark it so as to gain 10 per cent.; what price must he put on it? (,50 x 110=$,55, Ans.) What price must he put on it to gain 4 per cent.? 8 per cent.? 20 per cent? 77. William bought a sled for $3, and sold it so as to gain 10 per cent.; what did he get for it? Exercises for the Slate. 1. Bought 1 gallon of molasses for 623 cents, 1 quarter of flour for $1,121, 3 lbs. of tea for $1,05, 3 yards of flannel for $,874, and 1 skein of silk for 64 cents; what was the amount of the whole ? A. $3,732. 2. Bought 144 lbs. of raisins for $16; what was that a pound? A. $,1117. 3. What is the cost of 3600 yards of flannel, at $,12 a yard? (450) At $33? (1200) At $,20? (720) A. $2370. 4. In 20 lbs. of silver, how many spoons, each weighing 5 oz. 10 pwt.? A. 43 spoons, and 3 oz. 10 pwt. rem. 5. A bought 4 hogsheads of molasses for $84, sold 1 hogshead for $25, and the remainder at the rate of 4 cents a pint; how much did he make on the whole? A. $1,48. 6. Bought a hogshead of sugar, weighing 12 cwt. 1 qr. 15 lbs., and sold at one time 2 cwt. 2 qrs. 8 lbs, at another, 5 cwt. 15 lbs., and at another, I ewt. 3 qrs.; how much remained unsold? A. 2 cwt. 3 qrs. 20 lbs. 7. Multiply by 7. A. 21. 8. Divide by . A.. 9. Multiply by 2. A. 1. 10. Divide by 2. A. 불=1층. 11. There are 4 pieces of cloth, one containing 8 yds., another 16 yds., another 124 yds., and another 73 yds.; how many yards in the 4 pieces? A. 44 yds. 3 qrs. 3 na. 12. What is the difference between and ? A. Z... Between and ? A. . Between and 1? A. 16. 13. Reduce of a guinea to the fraction of a pound. A. ‡. 14. What is the value of ,003125£? A. 3 qrs. 15. How much does ,025 make multiplied by,325? (8125) By Too? (6) By 3130? (7675) By 276? (69) By 25todʊo? (6250125) A. 7,6104875. 500 16. A farmer sent a load of hay to market, which, with the cart, weighed 29 cwt. 3 qrs. 16 lbs.; the weight of the cart was 103 cwt.; what did the hay come to, at $15 a ton? A. $14,357 +. 17. A merchant bought sugar in a hogshead, both of which weighed 8 cwt. 15 lbs.; the hogshead alone weighed 1 cwt. 1 qr.; what was the cost of the sugar, at 114 cents a pound? A. $86,733. The two preceding questions are proper examples in a rule usually termed Tare and Trett. 18. Bought 50 yards of broadcloth for $160,50, but, not proving so good as I expected, I am willing to lose $42 on the sale of it; what must I demand per ell French? A. $3,555. 19. What is my demand for selling 600 bales of cotton, at $40 a bale, for 24 per cent. commission? (550125) For 4 per cent.? (110025) For 7 per cent.? (171150) For 5 per cent. > (13141875) A. $4676,064. 20. What is the interest of $200,50 for 2 yrs. 6 mo.? (30075) For 5 yrs. 3 mo. 15 days? (63658) For 6 mo.? (6516) For 1 yr. 3 mo. 19 days? (15672) A. $115,921. 21. What is the difference between the compound and simple interest of $200 for 1 yr. 6 mo.? (36) For 3 yrs. 4 mo.? (2967) For 2 yrs. 6 mo. 15 days? (1523) 9. $4,85. 22. What is the amount of $60 for 10 yrs. 3 mo. 19 days? (9709) For 8 yrs. 9 mo. 9 days?" (9159) ́A. $188,68. 23. Bought calico for 25 cts. a yard; how must I mark it so as to gain 10 per cent. on each yard? (275) 12 per cent. ? (28) 15 per cent.? (287) 20 per cent.? (30) A. $1,142. 24. What is the difference between the discount of $227,66 for 2 yrs. 3 mo. 20 days, and the interest of the same sum for the same time? A. $3,832. 25. Which is the most, the compound interest of $520 for 5 yrs., or the discount of the same sum for the same time? A. Compound interest, by $55,877. 26. If 300 men, in 6 months, perform a piece of work when the days are 12 hours long, how many men will do the same in 4 months, when the days are only 8 hours long? A. 675 men. 27. What is the difference of time between April 1st, 1826, and June 15th, 1829? (3,2,14) Between March 19th, 1829, and August 20, 1826? (2,6,29) Between July 5, 1800, and February 16, 1826? (25,7,11) A. 31 yrs., 4 mo., 24 days. 23. What is the interest of $120,60, from June 1, 1828, to June 16, 1829? (7537) From May 15, 1824, to August 29, 1830? (45506) From October 10, 1825, to November 1, 1828? (2213) A. $75,173+. ¶ LXXV. In computing Interest on Notes, When a settlement is made within a short time from the date or commencement of interest, it is generally the custom to proceed according to the following RULE. Find the amount of the principal, from the time the interest I commenced to the time of settlement, and likewise the amount of each payment, from the time it was paid to the time of settlement; then deduct the amount of the several payments from the amount of the principal. Exercises for the Slate. 1. For value received, I promise to pay Rufus Stanly, or order, Three Hundred Dollars, with interest. April 1, 1825. $300. On this note were the following endorsements:- PETER MOSELY. Time. April 16, 1826, $50 3, 2, 6, 1, 11, 15, 4. What was due April 1, 1828? Ans., $60,73. $120 CALCULATION. The first principal on interest from April 1, 1825, Interest to April 1, 1828, (36 mo.), Amount of principal First payment, Oct. 1, 1825, . Third payment, Dec. 1, 1827, $100,00 15,00 50,00 5,87 120,00 2,40 Interest to April 1, 1828, (4 mo.) • 2. For value received, I promise to pay Peter Trusty, or order, Five Hundred Dollars, with interest. July 1, 1825. $500. JAMES CARELESS. Time $120 $180 3, 1, 10, March 16, 1821, received $600, What remained due Jan. 16, 1823? Ans., $203,50. Many have discarded the preceding rule, under a false impression that it does not proceed on the ground of simple interest; in other words, that the "interest" (allowed the debtor) "will, in a course of years, completely expunge, or, as it may be said, eat up the debt." This objection, as it respects simple interest, it is believed, may be completely obviated. We will cite an example, which is generally considered as illustrating this objection in a forcible manner : A lends B 100 dollars, at 6 per cent. interest, and takes his note of hand. B does no more than pay A at every year's end 6 dollars (which is then justly due to B for the use of his money), and has it endorsed on his note. At the end of 10 years, B takes up his note, and the sum he has to pay is reckoned thus:—the principal, 100 dollars, on interest 10 years, amounts to 160 deilars; there are nine endorsements, of 6 dollars each, upon which the debtor claims interest; one for 9 years, the second for 8 years, the third for 7 years, and so down to the time of settlement; the whole amount of the several endorsements and their interest (as any one may see by casting it), is $70, 20 cts.; this, subtracted from 160 dollars, the amount of the debt, leaves, in favour of the creditor, $89, 40 cts., or $10,20 cts. less than the original principal, of which he has not received a cent, but only its annual interest. Extend it to 28 years, and A, the creditor, would fall in debt to B, without receiving a cent of the 100 dollars which he lent him. In this example, in the first place, there is not actually due A $6 at each year's end, to be by him put out at interest; for this would be more than simple interest. In the next place, the objection proceeds on the supposition that the annual endorsements of $6 were closely locked up in A's coffers, or lying dormant; for, had the $6 been put out at interest, as it might have been, the amount of it would of course be the same as the amount of the endorsements: hence the principal of the note would remain in reality unimpaired. In this way B gets interest for the money advanced or endorsed, and A loses nothing by it, for the payments are at his disposal. The correctness of this rule may be fur ther illustrated by the same example. If the $6 interest be reserved, and the payment of $6 be deducted yearly from the principal, the interest being east on the remainder at every year's end, and reserved as before, then, at the time of settlement, A could not reasonably claim any more, on the ground of simple interest, than what remained of the principal, and the sum of the interest of the principal from time to time, added together. For it certainly is not reasonable that he should have interest on any more principal than he actually had during the whole time. This process produces the same result as the former. Hence we infer, that, if the preceding rule be correct on the ground of simple interest (which must be allowed from the preceding facts), it follows, that any other mode, producing a different result from this, must be incorrect. The Connecticut and Massachusetts rules, which are by law established, produce results widely different from the above, and that, too, in favour of the lender. They must, then, give the lender more than simple interest, that is, > compound; which is not recognised by statute of either state, and which, it is said, the law specially guards against-a strange discrepancy in legislative enactments. We can illustrate this best by a practical example : Messrs. Brown and Ives, Providence, loan to government $200000 at 6 per cent. interest: the avails of the post office in said town, being about $1000, are to be annually applied to the payment of the debt, and to operate as endorsements. The interest of $200000 for one year is $12000, and the amount, $212000. Then, by the Connecticut mode, the payment of $1000 is to be deducted from $212000, which leaves $211000 on interest for the 2d year; "that is, $11000 more than the original debt immediately accumulating interest, besides the $1000, which is at their disposal. Here, then, it may be asked, what is this but interest on interest, that is, compound interest? The Massachusetts mode is equally as incorrect as the Connecticut, if not more so; for, by that, the principal is permitted to accumulate interest, till the payment, or sum of the payments, is equal to the interest then due; in which case the payments are to lie dormant, be they ever so many, and ever so large; and to remain so till the time of settlement, be it at ever so remote a period. But when the sum of the payments is equal to the interest then due, it is first to cancel an equal sum of interest, thereby placing the payment at the disposal of the lender, which he can, if he chooses, put at interest, while the borrower gets nothing at all for the use of his money, provided it does not at any time exceed the interest. In this way, the lender most surely gets interest on interest, that is, compound interest. Under such circumstances, it would be politic in the borrower not to make any payments at all; for, as sure as he does, if it is not more than one cent, and has it endorsed on the note, by the Connecticut mode, the interest of one year is immediately incorporated with the principal, both drawing interest, compounding the interest yearly, provided payments are made yearly. By the Massachusetts mode, the lender would have the interest on any sum of endorsements less than the interest till the time of settlement, while the interest is running on against the borrower; and when it is equal, it is to be placed in the hands of the lender, which he may put at interest, if he chooses. From the preceding remarks it is fairly to be inferred, that the borrower would find it for his advantage to deposit his payments in the Savings' Bank at 5 per cent. interest, instead of making endorsements, and thus continue to do till he is able to pay the note with the interest. It would also be for the advantage of the lender even to hire the borrower to make endorsements as frequent as possible. By the Connecticut mode, the trifling sum of $1, endorsed on a note, may, in many cases, be equivalent to the annual rent of 20 brick buildings, or more, in Broadway, in the city of New York. These rules, however, although not on the ground of simple interest, must have a place, as they are established by law. MASSACHUSETTS RULE. Compute the interest on the principal sum to the first time when a payment was made, which, either alone, or together with the preceding payments (if any), exceeds the interest then due; add that interest to the principal, and from the sum subtract the payment, or the sum of the payments, made at that time, and the remainder will be a new principal, with which proceed as with the first principal, and so on, to the time of settlement." 1. For value received, I promise to pay Jason Park, er order, Six Hundred Dollars, with interest. March 1, 1822. STEPHEN STIMPSON. $600. |